Flowers adorn a grave at a cemetery in Gaza City, in the northern Gaza Strip, Monday, July 28, 2014.

Lefteris Pitarakis/AP

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A pseudo cease-fire in the Gaza Strip continued in fits and starts on the first day of the Muslim holiday of Eid al-Fitr, but neither Israeli nor Palestinian forces appear willing to submit to international pressure for an unconditional halt in fighting.

Israeli and Palestinian forces exchanged fire intermittently this morning, bringing an end to a nearly 12-hour lull that began around 9:30 p.m. Sunday, the Associated Press reports. The Israeli military said it fired at two rocket launchers and a rocket manufacturing site in Gaza after Palestinians launched a rocket at the Israeli city of Ashkelon, north of Gaza. The rocket caused no damage or injuries.

But the fighting appears to have largely stalled today, the start of the three-day festival of Eid al-Fitr, which marks the end of the fasting month of Ramadan. Israeli Military Spokesman Gen. Moti Almoz called the overnight pause an "unlimited lull," though he noted that Israeli forces continued to attack and destroy border tunnels into Gaza, Agence France-Presse reports. AP cited a similar statement today from the military: "Quiet will be met with quiet."

More than 1,000 Palestinians have been killed in the conflict, which started on July 8 and expanded to a ground operation on July 17, as well as 43 Israel Defense Force soldiers and three Israeli residents.

At a midnight meeting of the United Nations Security Council, the 15-member body pushed for "an immediate and unconditional humanitarian ceasefire, allowing for the delivery of urgently needed assistance, and they urged all parties to accept and fully implement the humanitarian ceasefire into the Eid period and beyond." Though non-binding, the statement is the Security Council's strongest so far.

The statement echoes a demand made by President Obama in a phone call to Israeli Prime Minister Benjamin Netanyahu on Sunday, calling for a cease-fire and long-term solution that must allow "Palestinians in Gaza to lead normal lives" and "must ensure the disarmament of terrorist groups and the demilitarization of Gaza," writes the BBC.

The Christian Science Monitor writes that Hamas fears the ongoing, stuttering cease-fires play into the hands of Israel. Hamas wants a long-term cease-fire agreement to include the lifting of the Israeli and Egyptian blockade on Gaza. But allowing Israel to continue destroying Hamas tunnels without discussion of its cease-fire demands, “is not what the Palestinian people are looking for,” Hamas spokesman Ehab Al Ghossein said.

Mkheimer Abu Saada, a political science professor at Al Aqsa University in Gaza, said Hamas will not agree to an extension of short-term truces because it wants to show that the decision to end the conflict can't be taken by Israel unilaterally, and it is afraid that Israel is trying to bypass negotiations on an enduring agreement. “[Israel is] trying to push Hamas and Palestinians into an extension of the ceasefire without [fulfilling] Palestinian demands and Palestinian ambitions,” he said. “They're taking Palestinians back to square one after this heavy price of death and destruction."

The BBC notes that there is little appetite for a cease-fire among the Israeli public, which is afraid of the threat brought by the Gazan tunnel network. Some 87 percent of Israelis are in favor of the operation, reports the BBC's Bethany Bell. Israel's rocket defenses may minimize the risk of overhead dangers, one woman told her, "But there's no Iron Dome protection against Hamas fighters coming up through the tunnels to kidnap and kill us."